You also need to take y''. Solving for y' = 0 just gets you the values of y for which the slope is zero. To also learn whether those points are (relative) minima or maxima requires taking y'' and substituting the values of y for which y' = 0.

You also need to take y''. Solving for y' = 0 just gets you the values of y for which the slope is zero. To also learn whether those points are (relative) minima or maxima requires taking y'' and substituting the values of y for which y' = 0.

Odd that oay should be ruder than rude man and then rude man agrees with him! But oay is right- the second derivative is irrelevant. You are NOT asked to find "inflection points".

y'= y3- y2- 12y= y(y2- y- 12)= y(y- 4)(y+ 3), then if y< -3, all three factors are negative so y' is negative. If -3< y< 0 then y+3 is positive while y and y= 4 are both negative so y' is positive, etc.

But you would still need to find what values of t give those values of y.

Apt comment gracefully accepted and, shall I say, "wittily" replied to. I worry a lot less about rudeness when replying to somebody with 1600+ posts under their belt. I assume that's made them at least a little bit thick skinned. Nice exchange. I don't think there was any real rudeness intended and better yet, none recieved.